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    "# 循环神经网络\n",
    "\n",
    "目录\n",
    "\n",
    "- 序列模型\n",
    "- 文本预处理\n",
    "- 语言模型和数据集\n",
    "- 循环神经网络从零开始实现\n",
    "- 循环神经网络的简洁实现"
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    "## 序列模型\n",
    "\n",
    "使用正弦函数和一些可加性噪声来生成序列数据，时间步为$1, 2, \\ldots, 1000$"
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   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l\n",
    "\n",
    "T = 1000\n",
    "time = torch.arange(1, T + 1, dtype=torch.float32)\n",
    "x = torch.sin(0.01 * time) + torch.normal(0, 0.2, (T,))\n",
    "d2l.plot(time, [x], 'time', 'x', xlim=[1, 1000], figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40016f4b-419b-4e8c-9f08-683954e4a879",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将数据映射为数据对$y_t = x_t$和$\\mathbf{x}_t = [x_{t-\\tau}, \\ldots, x_{t-1}]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4a297c5d-5576-4561-95eb-2912de6ff393",
   "metadata": {
    "origin_pos": 9,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "tau = 4 # Markov 链长度\n",
    "features = torch.zeros((T - tau, tau)) # x_t\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: T - tau + i] # 顺延一个位置\n",
    "labels = x[tau:].reshape((-1, 1)) # y_t\n",
    "\n",
    "batch_size, n_train = 16, 600\n",
    "# 只有前n_train个样本用于训练\n",
    "train_iter = d2l.load_array((features[:n_train], labels[:n_train]),\n",
    "                            batch_size, is_train=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d30984f6-b1e0-4184-bfb4-3850b34b72f7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "使用一个相当简单的架构训练模型：\n",
    "一个拥有两个全连接层的多层感知机"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "01306b9f-8e94-41ab-a946-e61d2125871a",
   "metadata": {
    "origin_pos": 12,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def init_weights(m):\n",
    "    if type(m) == nn.Linear:\n",
    "        nn.init.xavier_uniform_(m.weight)\n",
    "\n",
    "def get_net():\n",
    "    \"\"\"两个全连接层的多层感知机\"\"\"\n",
    "    net = nn.Sequential(nn.Linear(4, 10),\n",
    "                        nn.ReLU(),\n",
    "                        nn.Linear(10, 1))\n",
    "    net.apply(init_weights)\n",
    "    return net\n",
    "\n",
    "loss = nn.MSELoss(reduction='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "276e9d4d-a27c-4604-84b3-1f86210610ba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "efcaf6c4-98ab-41b9-9d88-1b8b8f3a2320",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss: 0.075906\n",
      "epoch 2, loss: 0.057385\n",
      "epoch 3, loss: 0.055220\n",
      "epoch 4, loss: 0.053874\n",
      "epoch 5, loss: 0.054573\n"
     ]
    }
   ],
   "source": [
    "def train(net, train_iter, loss, epochs, lr):\n",
    "    trainer = torch.optim.Adam(net.parameters(), lr)\n",
    "    for epoch in range(epochs):\n",
    "        for X, y in train_iter:\n",
    "            trainer.zero_grad()\n",
    "            l = loss(net(X), y)\n",
    "            l.sum().backward()\n",
    "            trainer.step()\n",
    "        print(f'epoch {epoch + 1}, '\n",
    "              f'loss: {d2l.evaluate_loss(net, train_iter, loss):f}')\n",
    "\n",
    "net = get_net()\n",
    "train(net, train_iter, loss, 5, 0.01)\n",
    "# 损失值上升？训练瓶颈，或学习率偏大"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21a70294-3f5d-40a0-bacc-267f4b7c4930",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "单步预测：模型预测下一个时间步。注意：600+4（n_train + tau）之后都是预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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   "metadata": {
    "origin_pos": 19,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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   "source": [
    "onestep_preds = net(features) # features[:, i] = x[i: T - tau + i]\n",
    "d2l.plot([time, time[tau:]],\n",
    "         [x.detach().numpy(), onestep_preds.detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds'], xlim=[1, 1000],\n",
    "         figsize=(6, 3))"
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   "source": [
    "多步预测：604之后预测很快衰减到常数，主要由于误差的累计"
   ]
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  {
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    "tab": [
     "pytorch"
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   ],
   "source": [
    "multistep_preds = torch.zeros(T)\n",
    "multistep_preds[: n_train + tau] = x[: n_train + tau]\n",
    "for i in range(n_train + tau, T):\n",
    "    multistep_preds[i] = net( # 当前预测基于之前的预测结果\n",
    "        multistep_preds[i - tau:i].reshape((1, -1)))\n",
    "\n",
    "d2l.plot([time, time[tau:], time[n_train + tau:]],\n",
    "         [x.detach().numpy(), onestep_preds.detach().numpy(),\n",
    "          multistep_preds[n_train + tau:].detach().numpy()], 'time',\n",
    "         'x', legend=['data', '1-step preds', 'multistep preds'],\n",
    "         xlim=[1, 1000], figsize=(6, 3))"
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  {
   "cell_type": "markdown",
   "id": "cf285180-36e2-4579-bb96-b268e4d4907c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "更仔细地看一下$k$步预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77c62fa3-ef37-47e1-a3c2-f65cc0959150",
   "metadata": {
    "origin_pos": 28,
    "tab": [
     "pytorch"
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   },
   "outputs": [],
   "source": [
    "max_steps = 64\n",
    "\n",
    "features = torch.zeros((T - tau - max_steps + 1, tau + max_steps))\n",
    "# 列i（i<tau）是来自x的观测，其时间步从（i+1）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau):\n",
    "    features[:, i] = x[i: i + T - tau - max_steps + 1]\n",
    "\n",
    "# 列i（i>=tau）是来自（i-tau+1）步的预测，其时间步从（i+1）到（i+T-tau-max_steps+1）\n",
    "for i in range(tau, tau + max_steps):\n",
    "    features[:, i] = net(features[:, i - tau:i]).reshape(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3d25e582-80f2-4b88-824c-92a3175693b6",
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    "origin_pos": 28,
    "slideshow": {
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    "tab": [
     "pytorch"
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   "outputs": [
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      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
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     "output_type": "display_data"
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   ],
   "source": [
    "steps = (1, 4, 16, 64)\n",
    "d2l.plot([time[tau + i - 1: T - max_steps + i] for i in steps],\n",
    "         [features[:, (tau + i - 1)].detach().numpy() for i in steps], 'time', 'x',\n",
    "         legend=[f'{i}-step preds' for i in steps], xlim=[5, 1000],\n",
    "         figsize=(6, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b70f006-4f0b-44cf-960d-19c2eeca5b4e",
   "metadata": {
    "slideshow": {
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    },
    "tags": []
   },
   "source": [
    "## 文本预处理\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ee92af9b-d39a-4036-a6ff-38601e7f02b4",
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import collections\n",
    "import re\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f84c0c18-28d3-4bdc-8467-f82f23803a39",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将数据集读取到由多条文本行组成的列表中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e38932bf-39bd-4b43-8feb-78a3d5e90bdf",
   "metadata": {
    "origin_pos": 5,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# 文本总行数: 3221\n",
      "the time machine by h g wells\n",
      "twinkled and his usually pale face was flushed and animated the\n"
     ]
    }
   ],
   "source": [
    "d2l.DATA_HUB['time_machine'] = (d2l.DATA_URL + 'timemachine.txt',\n",
    "                                '090b5e7e70c295757f55df93cb0a180b9691891a')\n",
    "\n",
    "def read_time_machine():  \n",
    "    \"\"\"将时间机器数据集加载到文本行的列表中\"\"\"\n",
    "    with open(d2l.download('time_machine'), 'r') as f:\n",
    "        lines = f.readlines()\n",
    "    return [re.sub('[^A-Za-z]+', ' ', line).strip().lower() for line in lines]\n",
    "\n",
    "lines = read_time_machine()\n",
    "print(f'\n",
    "print(lines[0])\n",
    "print(lines[10])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f7891ef-5a67-4407-ab73-711901c9360a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "文本序列拆分成词元列表：词元（token）是文本的基本单位"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "120b451f-f16a-4bd7-b105-7b88de2a5e2a",
   "metadata": {
    "origin_pos": 7,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
      "[]\n",
      "[]\n",
      "[]\n",
      "[]\n",
      "['i']\n",
      "[]\n",
      "[]\n",
      "['the', 'time', 'traveller', 'for', 'so', 'it', 'will', 'be', 'convenient', 'to', 'speak', 'of', 'him']\n",
      "['was', 'expounding', 'a', 'recondite', 'matter', 'to', 'us', 'his', 'grey', 'eyes', 'shone', 'and']\n",
      "['twinkled', 'and', 'his', 'usually', 'pale', 'face', 'was', 'flushed', 'and', 'animated', 'the']\n"
     ]
    }
   ],
   "source": [
    "def tokenize(lines, token='word'):  \n",
    "    \"\"\"将文本行拆分为单词或字符词元\"\"\"\n",
    "    if token == 'word':\n",
    "        return [line.split() for line in lines]\n",
    "    elif token == 'char':\n",
    "        return [list(line) for line in lines]\n",
    "    else:\n",
    "        print('错误：未知词元类型：' + token)\n",
    "\n",
    "tokens = tokenize(lines)\n",
    "for i in range(11):\n",
    "    print(tokens[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b31663a-577a-4565-9a32-88476c497da5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "构建一个字典，通常也叫做*词表*（vocabulary），\n",
    "用来将字符串类型的词元映射到从$0$开始的数字索引中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99739e5c-8836-4707-94c3-acea573eb39d",
   "metadata": {
    "origin_pos": 9,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class Vocab:  \n",
    "    \"\"\"文本词表\"\"\"\n",
    "    def __init__(self, tokens=None, min_freq=0, reserved_tokens=None):\n",
    "        if tokens is None:\n",
    "            tokens = []\n",
    "        if reserved_tokens is None:\n",
    "            reserved_tokens = []\n",
    "        # 按出现频率排序\n",
    "        counter = count_corpus(tokens) # 下页\n",
    "        self._token_freqs = sorted(counter.items(), key=lambda x: x[1],\n",
    "                                   reverse=True)\n",
    "        # 未知词元的索引为0\n",
    "        self.idx_to_token = ['<unk>'] + reserved_tokens\n",
    "        self.token_to_idx = {token: idx\n",
    "                             for idx, token in enumerate(self.idx_to_token)}\n",
    "        for token, freq in self._token_freqs:\n",
    "            if freq < min_freq:\n",
    "                break\n",
    "            if token not in self.token_to_idx:\n",
    "                self.idx_to_token.append(token)\n",
    "                self.token_to_idx[token] = len(self.idx_to_token) - 1\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.idx_to_token)\n",
    "\n",
    "    def __getitem__(self, tokens):\n",
    "        if not isinstance(tokens, (list, tuple)):\n",
    "            return self.token_to_idx.get(tokens, self.unk)\n",
    "        return [self.__getitem__(token) for token in tokens]\n",
    "\n",
    "    def to_tokens(self, indices):\n",
    "        if not isinstance(indices, (list, tuple)):\n",
    "            return self.idx_to_token[indices]\n",
    "        return [self.idx_to_token[index] for index in indices]\n",
    "\n",
    "    @property\n",
    "    def unk(self): # 未知词元的索引为0\n",
    "        return 0\n",
    "\n",
    "    @property\n",
    "    def token_freqs(self):\n",
    "        return self._token_freqs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "489af471-21c7-4d0d-a44b-eb57c0c94a80",
   "metadata": {
    "origin_pos": 9,
    "slideshow": {
     "slide_type": "slide"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def count_corpus(tokens):  \n",
    "    \"\"\"统计词元的频率\"\"\"\n",
    "    # 这里的tokens是1D列表或2D列表\n",
    "    if len(tokens) == 0 or isinstance(tokens[0], list):\n",
    "        # 将词元列表展平成一个列表\n",
    "        tokens = [token for line in tokens for token in line]\n",
    "    return collections.Counter(tokens)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc7064d3-a223-412d-9760-60f325d19841",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "构建词表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "23e10840-f076-4a54-a35f-519c383cfabc",
   "metadata": {
    "origin_pos": 11,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('<unk>', 0), ('the', 1), ('i', 2), ('and', 3), ('of', 4), ('a', 5), ('to', 6), ('was', 7), ('in', 8), ('that', 9)]\n"
     ]
    }
   ],
   "source": [
    "vocab = Vocab(tokens)\n",
    "print(list(vocab.token_to_idx.items())[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "761c8b7c-5a1e-4abd-8017-13076c0e961c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "将每一条文本行转换成一个数字索引列表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "57438103-9e5f-4209-b150-4879cbe3448d",
   "metadata": {
    "origin_pos": 13,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "文本: ['the', 'time', 'machine', 'by', 'h', 'g', 'wells']\n",
      "索引: [1, 19, 50, 40, 2183, 2184, 400]\n",
      "文本: ['twinkled', 'and', 'his', 'usually', 'pale', 'face', 'was', 'flushed', 'and', 'animated', 'the']\n",
      "索引: [2186, 3, 25, 1044, 362, 113, 7, 1421, 3, 1045, 1]\n"
     ]
    }
   ],
   "source": [
    "for i in [0, 10]:\n",
    "    print('文本:', tokens[i])\n",
    "    print('索引:', vocab[tokens[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46501e26-7258-42cc-ae51-f650ede4b7cc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将所有功能打包到`load_corpus_time_machine`函数中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1c8e17e7-4274-42bd-a92f-9d1d50d131c9",
   "metadata": {
    "origin_pos": 15,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(170580, 28)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def load_corpus_time_machine(max_tokens=-1):  \n",
    "    \"\"\"返回时光机器数据集的词元索引列表和词表\"\"\"\n",
    "    lines = read_time_machine()\n",
    "    # 使用字符（而不是单词）实现文本词元化\n",
    "    tokens = tokenize(lines, 'char')\n",
    "    vocab = Vocab(tokens)\n",
    "    # 数据集中每个文本行不一定是一个句子或一个段落，所以将所有文本行展平到一个列表中\n",
    "    corpus = [vocab[token] for line in tokens for token in line]\n",
    "    if max_tokens > 0:\n",
    "        corpus = corpus[:max_tokens]\n",
    "    return corpus, vocab\n",
    "\n",
    "corpus, vocab = load_corpus_time_machine()\n",
    "len(corpus), len(vocab)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "875ad793-5aa4-45a7-bae9-c05fbe802dd6",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "## 语言模型和数据集\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eaac119f-5878-469a-8563-7ff348c46d98",
   "metadata": {
    "origin_pos": 4,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('the', 2261),\n",
       " ('i', 1267),\n",
       " ('and', 1245),\n",
       " ('of', 1155),\n",
       " ('a', 816),\n",
       " ('to', 695),\n",
       " ('was', 552),\n",
       " ('in', 541),\n",
       " ('that', 443),\n",
       " ('my', 440)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l\n",
    "\n",
    "tokens = d2l.tokenize(d2l.read_time_machine())\n",
    "# 每个文本行不一定是一个句子或一个段落，因此把所有文本行拼接到一起\n",
    "corpus = [token for line in tokens for token in line]\n",
    "vocab = d2l.Vocab(corpus)\n",
    "vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6012d46b-3d2d-47f7-9baf-5f708fdaa720",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "频率高且无实意的词被称为*停用词*。画出的词频图：词频快速衰减"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "067d085c-c043-40e2-a4cb-628f58d9f5d2",
   "metadata": {
    "origin_pos": 6,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
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   ],
   "source": [
    "freqs = [freq for token, freq in vocab.token_freqs]\n",
    "d2l.plot(freqs, xlabel='token: x', ylabel='frequency: n(x)',\n",
    "         xscale='log', yscale='log')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0345b238-914f-49e0-ba2c-603fb149e5cd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "其他的词元组合，比如二元语法、三元语法等等，又会如何呢？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "67ba9fd3-dd1d-46da-9110-ddb151311043",
   "metadata": {
    "origin_pos": 8,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('of', 'the'), 309),\n",
       " (('in', 'the'), 169),\n",
       " (('i', 'had'), 130),\n",
       " (('i', 'was'), 112),\n",
       " (('and', 'the'), 109),\n",
       " (('the', 'time'), 102),\n",
       " (('it', 'was'), 99),\n",
       " (('to', 'the'), 85),\n",
       " (('as', 'i'), 78),\n",
       " (('of', 'a'), 73)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bigram_tokens = [pair for pair in zip(corpus[:-1], corpus[1:])]\n",
    "bigram_vocab = d2l.Vocab(bigram_tokens)\n",
    "bigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95568f8e-458c-47f5-984a-2284cb3fcdc4",
   "metadata": {},
   "source": [
    "注意：在十个最频繁的词对中，有九个是由两个停用词组成的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "43e05f91-63eb-4bd9-9fbd-ac46231195a8",
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    "origin_pos": 10,
    "slideshow": {
     "slide_type": "slide"
    },
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('the', 'time', 'traveller'), 59),\n",
       " (('the', 'time', 'machine'), 30),\n",
       " (('the', 'medical', 'man'), 24),\n",
       " (('it', 'seemed', 'to'), 16),\n",
       " (('it', 'was', 'a'), 15),\n",
       " (('here', 'and', 'there'), 15),\n",
       " (('seemed', 'to', 'me'), 14),\n",
       " (('i', 'did', 'not'), 14),\n",
       " (('i', 'saw', 'the'), 13),\n",
       " (('i', 'began', 'to'), 13)]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trigram_tokens = [triple for triple in zip(\n",
    "    corpus[:-2], corpus[1:-1], corpus[2:])]\n",
    "trigram_vocab = d2l.Vocab(trigram_tokens)\n",
    "trigram_vocab.token_freqs[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b386e37-25e1-4fd0-8215-a2f0eb9fab76",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "对比结论：单词序列都遵循齐普夫定律；N元组的数量不大，说明语言中存在相当多的结构；很多N元组很少出现，使得拉普拉斯平滑非常不适合语言建模"
   ]
  },
  {
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   "metadata": {
    "origin_pos": 12,
    "tab": [
     "pytorch"
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      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
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     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bigram_freqs = [freq for token, freq in bigram_vocab.token_freqs]\n",
    "trigram_freqs = [freq for token, freq in trigram_vocab.token_freqs]\n",
    "d2l.plot([freqs, bigram_freqs, trigram_freqs], xlabel='token: x',\n",
    "         ylabel='frequency: n(x)', xscale='log', yscale='log',\n",
    "         legend=['unigram', 'bigram', 'trigram'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07fc517f-e835-427b-9b07-572cda271200",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "随机生成小批量数据的特征、标签以供读取。随机采样子序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2b9ff3d9-5e25-4c7a-8c78-baa1841cd1ea",
   "metadata": {
    "origin_pos": 14,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def seq_data_iter_random(corpus, batch_size, num_steps):  \n",
    "    \"\"\"使用随机抽样生成一个小批量子序列\"\"\"\n",
    "    # 从随机偏移量开始对序列进行分区，随机范围包括num_steps-1\n",
    "    corpus = corpus[random.randint(0, num_steps - 1):]\n",
    "    # 减去1，是因为我们需要考虑标签（即当前预测）\n",
    "    num_subseqs = (len(corpus) - 1) // num_steps\n",
    "    # 长度为num_steps的子序列的起始索引\n",
    "    initial_indices = list(range(0, num_subseqs * num_steps, num_steps))\n",
    "    # 随机抽样中，来自两个相邻的、随机的、小批量中的子序列不一定在原始序列上相邻\n",
    "    random.shuffle(initial_indices)\n",
    "\n",
    "    def data(pos):\n",
    "        \"\"\"返回从pos位置开始的长度为num_steps的序列\"\"\"\n",
    "        return corpus[pos: pos + num_steps]\n",
    "\n",
    "    num_batches = num_subseqs // batch_size\n",
    "    for i in range(0, batch_size * num_batches, batch_size):\n",
    "        # 在这里，initial_indices包含子序列的随机起始索引\n",
    "        initial_indices_per_batch = initial_indices[i: i + batch_size]\n",
    "        X = [data(j) for j in initial_indices_per_batch]\n",
    "        Y = [data(j + 1) for j in initial_indices_per_batch]\n",
    "        yield torch.tensor(X), torch.tensor(Y) # 迭代器"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b58974a9-6884-4c6a-921e-74d46c3c17cd",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "生成一个从$0$到$34$的序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b872fee0-a08f-4d56-ae6d-c232706dd0d2",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:  tensor([[29, 30, 31, 32, 33],\n",
      "        [ 4,  5,  6,  7,  8]]) \n",
      "Y: tensor([[30, 31, 32, 33, 34],\n",
      "        [ 5,  6,  7,  8,  9]])\n",
      "X:  tensor([[ 9, 10, 11, 12, 13],\n",
      "        [14, 15, 16, 17, 18]]) \n",
      "Y: tensor([[10, 11, 12, 13, 14],\n",
      "        [15, 16, 17, 18, 19]])\n",
      "X:  tensor([[24, 25, 26, 27, 28],\n",
      "        [19, 20, 21, 22, 23]]) \n",
      "Y: tensor([[25, 26, 27, 28, 29],\n",
      "        [20, 21, 22, 23, 24]])\n"
     ]
    }
   ],
   "source": [
    "my_seq = list(range(35)) # 每组10个，最多采样3组\n",
    "for X, Y in seq_data_iter_random(my_seq, batch_size=2, num_steps=5):\n",
    "    print('X: ', X, '\\nY:', Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30f05cda-af02-4177-b810-596e157dbb2a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "保证两个相邻的小批量中的子序列在原始序列上也是相邻的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9af5e40f-5a79-402c-a810-4b5c0d738b60",
   "metadata": {
    "origin_pos": 18,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def seq_data_iter_sequential(corpus, batch_size, num_steps):  \n",
    "    \"\"\"使用顺序分区生成一个小批量子序列\"\"\"\n",
    "    # 从随机偏移量开始划分序列\n",
    "    offset = random.randint(0, num_steps)\n",
    "    num_tokens = ((len(corpus) - offset - 1) // batch_size) * batch_size\n",
    "    Xs = torch.tensor(corpus[offset: offset + num_tokens])\n",
    "    Ys = torch.tensor(corpus[offset + 1: offset + 1 + num_tokens])\n",
    "    Xs, Ys = Xs.reshape(batch_size, -1), Ys.reshape(batch_size, -1)\n",
    "    num_batches = Xs.shape[1] // num_steps\n",
    "    for i in range(0, num_steps * num_batches, num_steps):\n",
    "        X = Xs[:, i: i + num_steps]\n",
    "        Y = Ys[:, i: i + num_steps]\n",
    "        yield X, Y # 迭代器"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99250fbf-29b1-4f69-86cb-d991e0628808",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "读取每个小批量的子序列的特征`X`和标签`Y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "09c1d8ba-5770-4529-a0aa-8141e69d440e",
   "metadata": {
    "origin_pos": 21,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X:  tensor([[ 3,  4,  5,  6,  7],\n",
      "        [18, 19, 20, 21, 22]]) \n",
      "Y: tensor([[ 4,  5,  6,  7,  8],\n",
      "        [19, 20, 21, 22, 23]])\n",
      "X:  tensor([[ 8,  9, 10, 11, 12],\n",
      "        [23, 24, 25, 26, 27]]) \n",
      "Y: tensor([[ 9, 10, 11, 12, 13],\n",
      "        [24, 25, 26, 27, 28]])\n",
      "X:  tensor([[13, 14, 15, 16, 17],\n",
      "        [28, 29, 30, 31, 32]]) \n",
      "Y: tensor([[14, 15, 16, 17, 18],\n",
      "        [29, 30, 31, 32, 33]])\n"
     ]
    }
   ],
   "source": [
    "for X, Y in seq_data_iter_sequential(my_seq, batch_size=2, num_steps=5):\n",
    "    print('X: ', X, '\\nY:', Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fd09b29-9f9a-431c-9eca-98a67bfa0f3d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "将上面的两个采样函数包装到一个类中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2171a4b7-e026-4087-adfd-9b1883f0c2f9",
   "metadata": {
    "origin_pos": 23,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class SeqDataLoader:  \n",
    "    \"\"\"加载序列数据的迭代器\"\"\"\n",
    "    def __init__(self, batch_size, num_steps, use_random_iter, max_tokens):\n",
    "        if use_random_iter:\n",
    "            self.data_iter_fn = d2l.seq_data_iter_random\n",
    "        else:\n",
    "            self.data_iter_fn = d2l.seq_data_iter_sequential\n",
    "        self.corpus, self.vocab = d2l.load_corpus_time_machine(max_tokens)\n",
    "        self.batch_size, self.num_steps = batch_size, num_steps\n",
    "\n",
    "    def __iter__(self):\n",
    "        return self.data_iter_fn(self.corpus, self.batch_size, self.num_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf929e6c-8b4c-48c6-a66d-058d653d2cb9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "最后，我们定义了一个函数`load_data_time_machine`，\n",
    "它同时返回数据迭代器和词表"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2348d264-aa8b-42d8-a9f9-e1370fdebb78",
   "metadata": {
    "origin_pos": 25,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def load_data_time_machine(batch_size, num_steps,  \n",
    "                           use_random_iter=False, max_tokens=10000):\n",
    "    \"\"\"返回时光机器数据集的迭代器和词表\"\"\"\n",
    "    data_iter = SeqDataLoader(\n",
    "        batch_size, num_steps, use_random_iter, max_tokens)\n",
    "    return data_iter, data_iter.vocab"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1cb218c-7cf3-44c5-9bda-eae9a8a9ecc5",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    },
    "tags": []
   },
   "source": [
    "## 循环神经网络从零开始实现\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1a5c2509-2aac-4bc5-b1d6-c364e0319cf3",
   "metadata": {
    "origin_pos": 4,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "import torch\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size, num_steps = 32, 35\n",
    "train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9443aef4-43ce-416f-8d4c-d5f917b82adb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "独热编码：将词元编码为相互独立的单位向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "889aa7a8-59d4-4026-8a58-e2587e26be4b",
   "metadata": {
    "origin_pos": 8,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "         0, 0, 0, 0],\n",
       "        [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "         0, 0, 0, 0]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F.one_hot(torch.tensor([0, 2]), len(vocab)) # 28个词元"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea841674-0f3c-4d83-9e45-a2b48b7c90be",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "小批量数据形状是二维张量：\n",
    "（批量大小，时间步数）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "030e1183-8e22-4157-a96d-fc06b53cd1f8",
   "metadata": {
    "origin_pos": 12,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 2, 28])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.arange(10).reshape((2, 5))\n",
    "F.one_hot(X.T, 28).shape # （时间步数，批量大小，词表大小）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac0e9423-2a31-4ee4-bd29-f532d847fd9c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "初始化循环神经网络模型的模型参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "04638c3d-81a1-4dd0-b9a5-4336024f1518",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def get_params(vocab_size, num_hiddens, device):\n",
    "    num_inputs = num_outputs = vocab_size\n",
    "\n",
    "    def normal(shape):\n",
    "        return torch.randn(size=shape, device=device) * 0.01\n",
    "\n",
    "    # 隐藏层参数\n",
    "    W_xh = normal((num_inputs, num_hiddens))\n",
    "    W_hh = normal((num_hiddens, num_hiddens))\n",
    "    b_h = torch.zeros(num_hiddens, device=device)\n",
    "    # 输出层参数\n",
    "    W_hq = normal((num_hiddens, num_outputs))\n",
    "    b_q = torch.zeros(num_outputs, device=device)\n",
    "    params = [W_xh, W_hh, b_h, W_hq, b_q]\n",
    "    for param in params:\n",
    "        param.requires_grad_(True)\n",
    "    return params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "752a4d90-10e1-4eb9-adea-c57fedcb3215",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "一个`init_rnn_state`函数在初始化时返回隐状态"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "48ec7510-6392-4945-9474-ac78d6126caf",
   "metadata": {
    "origin_pos": 20,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def init_rnn_state(batch_size, num_hiddens, device):\n",
    "    # （批量大小，隐藏单元数）\n",
    "    return (torch.zeros((batch_size, num_hiddens), device=device), )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75c17104-143e-44bb-9421-c5532863a935",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "下面的`rnn`函数定义了如何在一个时间步内计算隐状态和输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "6804ce54-cf84-43aa-a9df-a428c4e42288",
   "metadata": {
    "origin_pos": 24,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def rnn(inputs, state, params):\n",
    "    # inputs的形状：(时间步数量，批量大小，词表大小)\n",
    "    W_xh, W_hh, b_h, W_hq, b_q = params\n",
    "    H, = state\n",
    "    outputs = []\n",
    "    # X的形状：(批量大小，词表大小)\n",
    "    for X in inputs:\n",
    "        # 当元素在实数上均匀分布时，函数tanh的平均值为0\n",
    "        H = torch.tanh(torch.mm(X, W_xh) + torch.mm(H, W_hh) + b_h)\n",
    "        Y = torch.mm(H, W_hq) + b_q\n",
    "        outputs.append(Y)\n",
    "    return torch.cat(outputs, dim=0), (H,)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a77be26-fef3-49d3-b762-9517698d8ff7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "创建一个类来包装这些函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a190ae84-bd64-42e3-87ef-df459859710d",
   "metadata": {
    "origin_pos": 28,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class RNNModelScratch: \n",
    "    \"\"\"从零开始实现的循环神经网络模型\"\"\"\n",
    "    def __init__(self, vocab_size, num_hiddens, device,\n",
    "                 get_params, init_state, forward_fn):\n",
    "        self.vocab_size, self.num_hiddens = vocab_size, num_hiddens\n",
    "        self.params = get_params(vocab_size, num_hiddens, device)\n",
    "        self.init_state, self.forward_fn = init_state, forward_fn\n",
    "\n",
    "    def __call__(self, X, state):\n",
    "        X = F.one_hot(X.T, self.vocab_size).type(torch.float32)\n",
    "        return self.forward_fn(X, state, self.params)\n",
    "\n",
    "    def begin_state(self, batch_size, device):\n",
    "        return self.init_state(batch_size, self.num_hiddens, device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73068fe7-dd1f-4046-9975-16069df2c693",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "检查输出是否具有正确的形状"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "36215e45-3840-49f7-ab6e-2176fbdbdfc2",
   "metadata": {
    "origin_pos": 32,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([10, 28]), 1, torch.Size([2, 512]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_hiddens = 512\n",
    "net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params,\n",
    "                      init_rnn_state, rnn)\n",
    "state = net.begin_state(X.shape[0], d2l.try_gpu())\n",
    "Y, new_state = net(X.to(d2l.try_gpu()), state)\n",
    "# 输出：（时间步数x批量大小，词表大小）\n",
    "# 隐状态：（批量大小，隐藏单元数）\n",
    "Y.shape, len(new_state), new_state[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901c45ab-e314-4e4a-b23d-50831246dfe1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "预测函数：生成`prefix`之后的新字符。注意：训练样本仅是`prefix`，远不能达到优化目的"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0eaccd55-08c6-4ffa-88a9-f1424aedb9a3",
   "metadata": {
    "origin_pos": 39,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'time traveller lfy lfy lf'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def predict_ch8(prefix, num_preds, net, vocab, device):  \n",
    "    \"\"\"在prefix后面生成新字符\"\"\"\n",
    "    state = net.begin_state(batch_size=1, device=device)\n",
    "    outputs = [vocab[prefix[0]]]\n",
    "    get_input = lambda: torch.tensor([outputs[-1]], device=device).reshape((1, 1))\n",
    "    for y in prefix[1:]: # 预热期：不预测，只更新隐变量参数\n",
    "        _, state = net(get_input(), state)\n",
    "        outputs.append(vocab[y])\n",
    "    for _ in range(num_preds): # 预测num_preds步\n",
    "        y, state = net(get_input(), state)\n",
    "        outputs.append(int(y.argmax(dim=1).reshape(1)))\n",
    "    return ''.join([vocab.idx_to_token[i] for i in outputs])\n",
    "\n",
    "# 还未训练网络：预测结果相对随机\n",
    "predict_ch8('time traveller ', 10, net, vocab, d2l.try_gpu())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f30cd458-ea9e-49b8-8a70-07f09fe86232",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "梯度裁剪\n",
    "$$\\mathbf{g} \\leftarrow \\min\\left(1, \\frac{\\theta}{\\|\\mathbf{g}\\|}\\right) \\mathbf{g}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "203b3b5d-6cf8-4790-b191-81707cc48462",
   "metadata": {
    "origin_pos": 43,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def grad_clipping(net, theta):  \n",
    "    \"\"\"裁剪梯度\"\"\"\n",
    "    if isinstance(net, nn.Module):\n",
    "        params = [p for p in net.parameters() if p.requires_grad]\n",
    "    else:\n",
    "        params = net.params\n",
    "    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))\n",
    "    if norm > theta:\n",
    "        for param in params:\n",
    "            param.grad[:] *= theta / norm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b316418d-61db-4e56-befa-6b222d737868",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义一个函数在一个迭代周期内训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9bf19e02-bfa0-49ab-930b-0b91eb71c00a",
   "metadata": {
    "origin_pos": 47,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_epoch_ch8(net, train_iter, loss, updater, device, use_random_iter):\n",
    "    \"\"\"训练网络一个迭代周期（定义见第8章）\"\"\"\n",
    "    state, timer = None, d2l.Timer()\n",
    "    metric = d2l.Accumulator(2) # 训练损失之和,词元数量\n",
    "    for X, Y in train_iter:\n",
    "        if state is None or use_random_iter:\n",
    "            # 在第一次迭代或使用随机抽样时初始化state\n",
    "            state = net.begin_state(batch_size=X.shape[0], device=device)\n",
    "        else:\n",
    "            if isinstance(net, nn.Module) and not isinstance(state, tuple):\n",
    "                state.detach_() # state对于nn.GRU是单个张量\n",
    "            else: # state对于nn.LSTM或对于从零开始实现的模型是张量元组\n",
    "                for s in state:\n",
    "                    s.detach_()\n",
    "        y = Y.T.reshape(-1)\n",
    "        X, y = X.to(device), y.to(device)\n",
    "        y_hat, state = net(X, state)\n",
    "        l = loss(y_hat, y.long()).mean()\n",
    "        if isinstance(updater, torch.optim.Optimizer):\n",
    "            updater.zero_grad()\n",
    "            l.backward()\n",
    "            grad_clipping(net, 1)\n",
    "            updater.step()\n",
    "        else:\n",
    "            l.backward()\n",
    "            grad_clipping(net, 1)\n",
    "            updater(batch_size=1) # 已经调用了mean函数\n",
    "        metric.add(l * y.numel(), y.numel())\n",
    "    return math.exp(metric[0] / metric[1]), metric[1] / timer.stop()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "675d99cd-4f74-4245-b244-950177e64c68",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "循环神经网络模型的训练函数既支持从零开始实现，\n",
    "也可以使用高级API来实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "98ee19b1-3584-4617-b78c-f9c24e641f62",
   "metadata": {
    "origin_pos": 51,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "def train_ch8(net, train_iter, vocab, lr, num_epochs, device,\n",
    "              use_random_iter=False):\n",
    "    \"\"\"训练模型（定义见第8章）\"\"\"\n",
    "    loss = nn.CrossEntropyLoss()\n",
    "    animator = d2l.Animator(xlabel='epoch', ylabel='perplexity',\n",
    "                            legend=['train'], xlim=[10, num_epochs])\n",
    "    if isinstance(net, nn.Module):\n",
    "        updater = torch.optim.SGD(net.parameters(), lr)\n",
    "    else:\n",
    "        updater = lambda batch_size: d2l.sgd(net.params, lr, batch_size)\n",
    "    predict = lambda prefix: predict_ch8(prefix, 50, net, vocab, device)\n",
    "    for epoch in range(num_epochs):\n",
    "        ppl, speed = train_epoch_ch8(\n",
    "            net, train_iter, loss, updater, device, use_random_iter)\n",
    "        if (epoch + 1) % 10 == 0:\n",
    "            print(predict('time traveller'))\n",
    "            animator.add(epoch + 1, [ppl])\n",
    "    print(f'困惑度 {ppl:.1f}, {speed:.1f} 词元/秒 {str(device)}')\n",
    "    print(predict('time traveller'))\n",
    "    print(predict('traveller'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eedbcfc6-3622-44b5-9702-ac0143ea247c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "现在，我们训练循环神经网络模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "116f5b2c-24cc-4042-8b72-fb5a0045a27e",
   "metadata": {
    "origin_pos": 54,
    "tab": [
     "pytorch"
    ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "困惑度 1.0, 67532.5 词元/秒 cuda:0\n",
      "time traveller with a slight accession ofcheerfulness really thi\n",
      "travelleryou can show black is white by argument said filby\n"
     ]
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    "num_epochs, lr = 500, 1\n",
    "train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu())"
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   "source": [
    "最后，让我们检查一下使用随机抽样方法的结果"
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   "execution_count": 16,
   "id": "b282297d-04cc-4370-a269-bb1a847d1f35",
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     "name": "stdout",
     "output_type": "stream",
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      "困惑度 1.4, 67608.9 词元/秒 cuda:0\n",
      "time travellerit s against reason said filbywan a gurently in th\n",
      "traveller after the pauserequired for the proper assimilati\n"
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   ],
   "source": [
    "net = RNNModelScratch(len(vocab), num_hiddens, d2l.try_gpu(), get_params,\n",
    "                      init_rnn_state, rnn)\n",
    "train_ch8(net, train_iter, vocab, lr, num_epochs, d2l.try_gpu(),\n",
    "          use_random_iter=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "808d4df7-8c2e-4f5f-95fe-0bb55ce8571b",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "## 循环神经网络的简洁实现\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "55f4c2e3-1602-4d14-bd63-b3834142148b",
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size, num_steps = 32, 35\n",
    "train_iter, vocab = d2l.load_data_time_machine(batch_size, num_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "844952af-89c0-4aaf-a4d1-3d1053c8d972",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "定义模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6a69aca1-8254-4a28-bc79-949b5e023aaa",
   "metadata": {
    "origin_pos": 6,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "num_hiddens = 256\n",
    "# 注意，rnn_layer只包含隐藏的循环层\n",
    "rnn_layer = nn.RNN(len(vocab), num_hiddens)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "803cc15e-eca9-42f5-9abf-972d50b8785d",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "使用张量来初始化隐状态"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "916cee3a-4078-45fc-a5ab-0a4e32f4eb5e",
   "metadata": {
    "origin_pos": 11,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 32, 256])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state = torch.zeros((1, batch_size, num_hiddens))\n",
    "state.shape # （隐藏层数，批量大小，隐藏单元数）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5287334-a64d-4d8f-918d-23342c037b24",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "通过一个隐状态和一个输入，我们就可以用更新后的隐状态计算输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "88e87cce-f70f-4539-9002-a12611749491",
   "metadata": {
    "origin_pos": 16,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([35, 32, 256]), torch.Size([1, 32, 256]))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.rand(size=(num_steps, batch_size, len(vocab)))\n",
    "# “输出”（Y）不涉及输出层的计算：它是指每个时间步的隐状态，\n",
    "# 这些隐状态可以用作后续输出层的输入\n",
    "Y, state_new = rnn_layer(X, state)\n",
    "Y.shape, state_new.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6faf827-63c5-47d5-9cb4-b0d8ab25e368",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "我们为一个完整的循环神经网络模型定义了一个`RNNModel`类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7f70156c-bf21-4bc4-906e-ff5852669cd5",
   "metadata": {
    "origin_pos": 20,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class RNNModel(nn.Module):\n",
    "    \"\"\"循环神经网络模型\"\"\"\n",
    "    def __init__(self, rnn_layer, vocab_size, **kwargs):\n",
    "        super(RNNModel, self).__init__(**kwargs)\n",
    "        self.rnn = rnn_layer\n",
    "        self.vocab_size = vocab_size\n",
    "        self.num_hiddens = self.rnn.hidden_size\n",
    "        # 如果RNN是双向的（之后将介绍），num_directions应该是2，否则应该是1\n",
    "        if not self.rnn.bidirectional:\n",
    "            self.num_directions = 1\n",
    "            self.linear = nn.Linear(self.num_hiddens, self.vocab_size)\n",
    "        else:\n",
    "            self.num_directions = 2\n",
    "            self.linear = nn.Linear(self.num_hiddens * 2, self.vocab_size)\n",
    "\n",
    "    def forward(self, inputs, state):\n",
    "        X = F.one_hot(inputs.T.long(), self.vocab_size)\n",
    "        X = X.to(torch.float32)\n",
    "        Y, state = self.rnn(X, state)\n",
    "        # 全连接层首先将Y的形状改为(时间步数*批量大小,隐藏单元数)\n",
    "        # 它的输出形状是(时间步数*批量大小,词表大小)。\n",
    "        output = self.linear(Y.reshape((-1, Y.shape[-1])))\n",
    "        return output, state\n",
    "\n",
    "    def begin_state(self, device, batch_size=1):\n",
    "        if not isinstance(self.rnn, nn.LSTM):\n",
    "            # nn.GRU以张量H作为隐状态\n",
    "            return  torch.zeros((self.num_directions * self.rnn.num_layers,\n",
    "                                 batch_size, self.num_hiddens),\n",
    "                                device=device)\n",
    "        else: # nn.LSTM以元组(H,C)作为隐状态\n",
    "            return (torch.zeros((\n",
    "                self.num_directions * self.rnn.num_layers,\n",
    "                batch_size, self.num_hiddens), device=device),\n",
    "                    torch.zeros((\n",
    "                        self.num_directions * self.rnn.num_layers,\n",
    "                        batch_size, self.num_hiddens), device=device))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4333f760-a48a-4038-b6ce-0a6cc408b028",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "基于随机权重初始化的模型进行预测：输出大量重复字符（类似之前人造数据`sin`函数的多步预测）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "16a236ef-aa2b-4d69-a65c-549e8dc79e96",
   "metadata": {
    "origin_pos": 24,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'time travellerpcpppppppp'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "device = d2l.try_gpu()\n",
    "net = RNNModel(rnn_layer, vocab_size=len(vocab))\n",
    "net = net.to(device)\n",
    "d2l.predict_ch8('time traveller', 10, net, vocab, device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "833326d0-c61e-48af-b5fa-718f44e65e95",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "使用高级API训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9b2d0ed1-0cdc-4b6b-989f-1c17e60ec2cb",
   "metadata": {
    "origin_pos": 28,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perplexity 1.3, 293417.9 tokens/sec on cuda:0\n",
      "time travellerif se gan ubsely fourth timethere is however a ten\n",
      "traveller and wheth dimensisnal fis liger an andeterall hey\n"
     ]
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    "num_epochs, lr = 500, 1\n",
    "d2l.train_ch8(net, train_iter, vocab, lr, num_epochs, device)"
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